Cosmic 21-cm Signal Research Articles

Exploring the likelihood of the 21-cm power spectrum with simulation-based inference

ABSTRACT Observations of the cosmic 21-cm power spectrum (PS) are starting to enable precision Bayesian inference of galaxy properties and physical cosmology, during the first billion years of our Universe. Here we investigate the impact of common approximations about the likelihood used in such inferences, including: (i) assuming a Gaussian functional form; (ii) estimating the mean from a single realization; and (iii) estimating the (co)variance at a single point in parameter space. We compare ‘classical’ inference that uses an explicit likelihood with simulation-based inference (SBI) that estimates the likelihood from a training set. Our forward models include: (i) realizations of the cosmic 21-cm signal computed with 21cmFAST by varying ultraviolet (UV) and X-ray galaxy parameters together with the initial conditions; (ii) realizations of the telescope noise corresponding to a $1000 \, \mathrm{h}$ integration with the low-frequency component of the Square Kilometre Array (SKA1-Low); and (iii) the excision of Fourier modes corresponding to a foreground-dominated horizon ‘wedge’. We find that the 1D PS likelihood is well described by a Gaussian accounting for covariances between wave modes and redshift bins (higher order correlations are small). However, common approaches of estimating the forward-modelled mean and (co)variance from a random realization or at a single point in parameter space result in biased and overconstrained posteriors. Our best results come from using SBI to fit a non-Gaussian likelihood with a Gaussian mixture neural density estimator. Such SBI can be performed with up to an order of magnitude fewer simulations than classical, explicit likelihood inference. Thus SBI provides accurate posteriors at a comparably low computational cost.

Exploring the cosmic 21-cm signal from the epoch of reionization using the wavelet scattering transform

ABSTRACT Detecting the cosmic 21-cm signal during the Epoch of Reionization and Cosmic Dawn will reveal insights into the properties of the first galaxies and advance cosmological parameter estimation. Until recently, the primary focus for astrophysical parameter inference from the 21-cm signal centred on the power spectrum (PS). However, the cosmic 21-cm signal is highly non-Gaussian rendering the PS suboptimal for characterizing the cosmic signal. In this work, we introduce a new technique to analyse the non-Gaussian information in images of the 21-cm signal called the Wavelet Scattering Transform (WST). This approach closely mirrors that of convolutional neural networks with the added advantage of not requiring tuning or training of a neural network. Instead, it compresses the 2D spatial information into a set of coefficients making it easier to interpret while also providing a robust statistical description of the non-Gaussian information contained in the cosmic 21-cm signal. First, we explore the application of the WST to mock 21-cm images to gain valuable physical insights by comparing to the known behaviour from the 21-cm PS. Then we quantitatively explore the WST applied to the 21-cm signal by extracting astrophysical parameter constraints using Fisher Matrices from a realistic 1000 h mock observation with the Square Kilometre Array. We find that: (i) the WST applied only to 2D images can outperform the 3D spherically averaged 21-cm PS, (ii) the excision of foreground contaminated modes can degrade the constraining power by a factor of ∼1.5–2 with the WST and (iii) higher cadences between the 21-cm images can further improve the constraining power.

Epoch of reionization parameter estimation with the 21-cm bispectrum

ABSTRACT We present the first application of the isosceles bispectrum to MCMC parameter inference from the cosmic 21-cm signal. We extend the MCMC sampler 21CMMC to use the fast bispectrum code, BiFFT, when computing the likelihood. We create mock 1000-h observations with SKA1-low, using pyObs21 to account for uv-sampling and thermal noise. Assuming the spin temperature is much higher than that of the cosmic microwave background, we consider two different reionization histories for our mock observations: fiducial and late-reionization. For both models we find that bias on the inferred parameter means and 1σ credible intervals can be substantially reduced by using the isosceles bispectrum (calculated for a wide range of scales and triangle shapes) together with the power spectrum (as opposed to just using one of the statistics). We find that making the simplifying assumption of a Gaussian likelihood with a diagonal covariance matrix does not notably bias parameter constraints for the three-parameter reionization model and basic instrumental effects considered here. This is true even if we use extreme (unlikely) initial conditions which would be expected to amplify biases. We also find that using the cosmic variance error calculated with Monte Carlo simulations using the fiducial model parameters while assuming the late-reionization model for the simulated data also does not strongly bias the inference. This implies we may be able to sparsely sample and interpolate the cosmic variance error over the parameter space, substantially reducing computational costs. All codes used in this work are publicly available.

Interpreting LOFAR 21-cm signal upper limits at z ≈ 9.1 in the context of high-z galaxy and reionization observations

ABSTRACT Using the latest upper limits on the 21-cm power spectrum at z ≈ 9.1 from the Low Frequency Array (LOFAR), we explore the regions of parameter space which are inconsistent with the data. We use 21cmmc, a Monte Carlo Markov chain sampler of 21cmfast which directly forward models the three dimensional (3D) cosmic 21-cm signal in a fully Bayesian framework. We use the astrophysical parametrization from 21cmfast, which includes mass-dependent star formation rates and ionizing escape fractions as well as soft-band X-ray luminosities to place limits on the properties of the high-z galaxies. Further, we connect the disfavoured regions of parameter space with existing observational constraints on the Epoch of Reionization such as ultra-violet (UV) luminosity functions, background UV photoionization rate, intergalactic medium (IGM) neutral fraction, and the electron scattering optical depth. We find that all models exceeding the 21-cm signal limits set by LOFAR at z ≈ 9.1 are excluded at ≳2σ by other probes. Finally, we place limits on the IGM spin temperature from LOFAR, disfavouring at 95 per cent confidence spin temperatures below ∼2.6 K across an IGM neutral fraction range of $0.15 \lesssim \bar{x}_{\rm H\, \rm {\small I}} \lesssim 0.6$. Note, these limits are only obtained from 141 h of data in a single redshift bin. With tighter upper limits, across multiple redshift bins expected in the near future from LOFAR, more viable models will be ruled out. Our approach demonstrates the potential of forward modelling tools such as 21cmmc in combining 21-cm observations with other high-z probes to constrain the astrophysics of galaxies.

A tale of two sites – I. Inferring the properties of minihalo-hosted galaxies from current observations

ABSTRACT The very first galaxies that started the cosmic dawn likely resided in so-called ‘minihaloes’, with masses of ∼105–$10^8{\, {\rm M}_\odot }$, accreting their gas from the intergalactic medium through H2 cooling. Such molecularly cooled galaxies (MCGs) mostly formed in pristine environments, hosted massive, metal-free stars, and were eventually sterilized by the build-up of a disassociating (Lyman–Werner; LW) background. Therefore, their properties might be very different from the galaxies we see in the later Universe. Although MCGs are probably too faint to be observed directly, we could nevertheless infer their properties from the imprint they leave in the cosmic 21-cm signal. Here we quantify this imprint by extending the public simulation code 21cmFAST to allow for a distinct population of MCGs. We allow MCGs to have different properties from other galaxies, including unique scaling relations for their stellar-to-halo mass ratios, ionizing escape fractions, and spectral energy distributions. We track inhomogeneous recombinations, disassociative LW feedback, and photoheating from reionization. After demonstrating how MCGs can shape the 21-cm signal, we explore to what extent current observations can already place constraints on their properties. The cosmic microwave background optical depth from Planck sets an upper limit on the product of the ionizing escape fraction and the stellar mass in MCGs. When including also the timing of the putative EDGES absorption signal, we find an additional strong degeneracy between the stellar mass and the X-ray luminosity of MCGs. If proven to be of cosmic origin, the timing of the EDGES signal would have been set by MCGs.

The effects of population III radiation backgrounds on the cosmological 21-cm signal

ABSTRACT We investigate the effects of Population III (Pop III) stars and their remnants on the cosmological 21-cm global signal. By combining a semi-analytic model of Pop III star formation with a global 21-cm simulation code, we investigate how X-ray and radio emission from accreting Pop III black holes may affect both the timing and depth of the 21-cm absorption feature that follows the initial onset of star formation during the Cosmic Dawn. We compare our results to the findings of the EDGES experiment, which has reported the first detection of a cosmic 21-cm signal. In general, we find that our fiducial Pop III models, which have peak star formation rate densities of ∼10−4 M⊙ yr−1 Mpc−3 between z ∼ 10 and z ∼ 15, are able to match the timing of the EDGES signal quite well, in contrast to models that ignore Pop III stars. To match the unexpectedly large depth of the EDGES signal without recourse to exotic physics, we vary the parameters of emission from accreting black holes (formed as Pop III remnants) including the intrinsic strength of X-ray and radio emission as well as the local column density of neutral gas. We find that models with strong radio emission and relatively weak X-ray emission can self-consistently match the EDGES signal, though this solution requires fine-tuning. We are only able to produce signals with sharp features similar to the EDGES signal if the Pop III IMF is peaked narrowly around $140 \, \mathrm{M}_\odot$.

Reionisation & Cosmic Dawn Astrophysics from the Square Kilometre Array: Impact of Observing Strategies

Abstract Interferometry of the cosmic 21-cm signal is set to revolutionise our understanding of the Epoch of Reionisation (EoR) and the Cosmic Dawn (CD). The culmination of ongoing efforts will be the upcoming Square Kilometre Array (SKA), which will provide tomography of the 21-cm signal from the first billion years of our Universe. Using a galaxy formation model informed by high-z luminosity functions, here we forecast the accuracy with which the first phase of SKA-low (SKA1-low) can constrain the properties of the unseen galaxies driving the astrophysics of the EoR and CD. We consider three observing strategies: (i) deep (1000h on a single field); (ii) medium-deep (100hr on 10 independent fields); and (iii) shallow (10hr on 100 independent fields). Using the 21-cm power spectrum as a summary statistic, and conservatively only using the 21-cm signal above the foreground wedge, we predict that all three observing strategies should recover astrophysical parameters to a fractional precision of ∼0.1 – 10 per cent. The reionisation history is recovered to an uncertainty of $\Delta z \mathrel {\lesssim}0.1$ (1σ) for the bulk of its duration. The medium-deep strategy, balancing thermal noise against cosmic variance, results in the tightest constraints, slightly outperforming the deep strategy. The shallow observational strategy performs the worst, with up to a ∼10 – 60 per cent increase in the recovered uncertainty. We note, however, that non-Gaussian summary statistics, tomography, as well as unbiased foreground removal would likely favour the deep strategy.

Inferring the astrophysics of reionization and cosmic dawn from galaxy luminosity functions and the 21-cm signal

The properties of the first galaxies, expected to drive the Cosmic Dawn (CD) and the Epoch of Reionization (EoR), are encoded in the 3D structure of the cosmic 21-cm signal. Parameter inference from upcoming 21-cm observations promises to revolutionize our understanding of these unseen galaxies. However, prior inference was done using models with several simplifying assumptions. Here we introduce a flexible, physically-motivated parametrization for high-$z$ galaxy properties, implementing it in the public code 21cmFAST. In particular, we allow their star formation rates and ionizing escape fraction to scale with the masses of their host dark matter halos, and directly compute inhomogeneous, sub-grid recombinations in the intergalactic medium. Combining current Hubble observations of the rest-frame UV luminosity function (UV LFs) at high-$z$ with a mock 1000h 21-cm observation using the Hydrogen Epoch of Reionization Arrays (HERA), we constrain the parameters of our model using a Monte Carlo Markov Chain sampler of 3D simulations, 21CMMC. We show that the amplitude and scaling of the stellar mass with halo mass is strongly constrained by LF observations, while the remaining galaxy properties are constrained mainly by 21-cm observations. The two data sets compliment each other quite well, mitigating degeneracies intrinsic to each observation. All eight of our astrophysical parameters are able to be constrained at the level of $\sim 10\%$ or better. The updated versions of 21cmFAST and 21CMMC used in this work are publicly available.

Reionization and Cosmic Dawn: theory and simulations

AbstractWe highlight recent progress in the sophistication and diversification of the simulations of cosmic dawn and reionization. The application of these modeling tools to recent observations has allowed us narrow down the timing of reionization. The midpoint of reionization is constrained to z = 7.6−0.7+0.8 (1 σ), with the strongest constraints coming from the optical depth to the CMB measured with the Planck satellite and the first detection of ongoing reionization from the spectra of the z = 7.1 QSOs ULASJ1120+0641. However, we still know virtually nothing about the astrophysical sources during the first billion years. The revolution in our understanding will be led by upcoming interferometric observations of the cosmic 21-cm signal. The properties of the sources and sinks of UV and X-ray photons are encoded in the 3D patterns of the signal. The development of Bayesian parameter recovery techniques, which tap into the wealth of the 21-cm signal, will soon usher in an era of precision astrophysical cosmology.

High Mass X-ray Binaries: Beacons in a Stormy Universe.

The discovery of gravity waves from the mergers of black hole binaries has focused the astronomical community on the high mass X-ray binaries (HMXBs) as the potential progenitors of close pairs of compact stars. This symposium gathered experts in observational and theoretical work for a very timely review of our understanding of the processes that drive the X-ray luminosity of the diverse kinds of binaries and what evolutionary stages are revealed in the observed cases. Here I offer a condensed summary of some of the results about massive star properties, the observational categories of HMXBs, their accretion processes, their numbers in the Milky Way and other galaxies, and how they may be related to the compact binaries that merge in a burst of gravity waves.

Constraining the redshifted 21-cm signal with the unresolved soft X-ray background

We use the observed unresolved cosmic X-ray background (CXRB) in the 0.5-2 keV band and existing upper limits on the 21-cm power spectrum to constrain the high-redshift population of X-ray sources, focusing on their effect on the thermal history of the Universe and the cosmic 21-cm signal. Because the properties of these sources are poorly constrained, we consider hot gas, X-ray binaries and mini-quasars (i.e., sources with soft or hard X-ray spectra) as possible candidates. We find that (1) the soft-band CXRB sets an upper limit on the X-ray efficiency of sources that existed before the end of reionization, which is one-to-two orders of magnitude higher than typically assumed efficiencies, (2) hard sources are more effective in generating the CXRB than the soft ones, (3) the commonly-assumed limit of saturated heating is not valid during the first half of reionization in the case of hard sources, with any allowed value of X-ray efficiency, (4) the maximal allowed X-ray efficiency sets a lower limit on the depth of the absorption trough in the global 21-cm signal and an upper limit on the height of the emission peak, while in the 21-cm power spectrum it sets a minimum amplitude and frequency for the high-redshift peaks, and (5) the existing upper limit on the 21-cm power spectrum sets a lower limit on the X-ray efficiency for each model. When combined with the 21-cm global signal, the CXRB will be useful for breaking degeneracies and helping constrain the nature of high-redshift heating sources.

Cross-correlation of the cosmic 21-cm signal and Lyman α emitters during reionization

Interferometry of the cosmic 21-cm signal is set to revolutionize our understanding of the Epoch of Reionization (EoR), eventually providing 3D maps of the early Universe. Initial detections however will be low signal-to-noise, limited by systematics. To confirm a putative 21-cm detection, and check the accuracy of 21-cm data analysis pipelines, it would be very useful to cross-correlate against a genuine cosmological signal. The most promising cosmological signals are wide-field maps of Lyman alpha emitting galaxies (LAEs), expected from the Subaru Hyper-Suprime Cam (HSC) Ultra-Deep field. Here we present estimates of the correlation between LAE maps at z~7 and the 21-cm signal observed by both the Low Frequency Array (LOFAR) and the planned Square Kilometer Array Phase 1 (SKA1). We adopt a systematic approach, varying both: (i) the prescription of assigning LAEs to host halos; and (ii) the large-scale structure of neutral and ionized regions (i.e. EoR morphology). We find that the LAE-21cm cross-correlation is insensitive to (i), thus making it a robust probe of the EoR. A 1000h observation with LOFAR would be sufficient to discriminate at >1 standard deviation a fully ionized Universe from one with a mean neutral fraction of xHI~0.50, using the LAE-21cm cross-correlation function on scales of R~3-10 Mpc. Unlike LOFAR, whose detection of the LAE-21cm cross-correlation is limited by noise, SKA1 is mostly limited by ignorance of the EoR morphology. However, the planned 100h wide-field SKA1-Low survey will be sufficient to discriminate an ionized Universe from one with xHI~0.25, even with maximally pessimistic assumptions.

The imprint of warm dark matter on the cosmological 21-cm signal

We investigate the effects of warm dark matter (WDM) on the cosmic 21-cm signal. If dark matter exists as WDM instead of cold dark matter (CDM), its non-negligible velocities can inhibit the formation of low-mass halos that normally form first in CDM models, therefore delaying star-formation. The absence of early sources delays the build-up of UV and X-ray backgrounds that affect the 21-cm radiation signal produced by neutral hydrogen. With use of the 21CMFAST, code, we demonstrate that the pre-reionization 21-cm signal can be changed significantly in WDM models with a free-streaming length equivalent to that of a thermal relic with mass mx of up to ~10-20 keV. In such a WDM cosmology, the 21-cm signal traces the growth of more massive halos, resulting in a delay of the 21-cm absorption signature and followed by accelerated X-ray heating. CDM models where astrophysical sources have a suppressed photon-production efficiency can delay the 21-cm signal as well, although its subsequent evolution is not as rapid as compared to WDM. This motivates using the gradient of the global 21-cm signal to differentiate between some CDM and WDM models. Finally, we show that the degeneracy between the astrophysics and mx can be broken with the 21-cm power spectrum, as WDM models should have a bias-induced excess of power on large scales. This boost in power should be detectable with current interferometers for models with mx < 3 keV, while next generation instruments will easily be able to measure this difference for all relevant WDM models.

Probing the first stars and black holes in the early Universe with the Dark Ages Radio Explorer (DARE)

A concept for a new space-based cosmology mission called the Dark Ages Radio Explorer (DARE) is presented in this paper. DARE’s science objectives include: (1) When did the first stars form? (2) When did the first accreting black holes form? (3) When did Reionization begin? (4) What surprises does the end of the Dark Ages hold (e.g., Dark Matter decay)? DARE will use the highly-redshifted hyperfine 21-cm transition from neutral hydrogen to track the formation of the first luminous objects by their impact on the intergalactic medium during the end of the Dark Ages and during Cosmic Dawn (redshifts z = 11–35). It will measure the sky-averaged spin temperature of neutral hydrogen at the unexplored epoch 80–420 million years after the Big Bang, providing the first evidence of the earliest stars and galaxies to illuminate the cosmos and testing our models of galaxy formation. DARE’s approach is to measure the expected spectral features in the sky-averaged, redshifted 21-cm signal over a radio bandpass of 40–120 MHz. DARE orbits the Moon for a mission lifetime of 3 years and takes data above the lunar farside, the only location in the inner solar system proven to be free of human-generated radio frequency interference and any significant ionosphere. The science instrument is composed of a low frequency radiometer, including electrically-short, tapered, bi-conical dipole antennas, a receiver, and a digital spectrometer. The smooth frequency response of the antennas and the differential spectral calibration approach using a Markov Chain Monte Carlo technique will be applied to detect the weak cosmic 21-cm signal in the presence of the intense solar system and Galactic foreground emissions.

21cmfast: a fast, seminumerical simulation of the high-redshift 21-cm signal

We introduce a powerful semi-numeric modeling tool, 21cmFAST, designed to efficiently simulate the cosmological 21-cm signal. Our code generates 3D realizations of evolved density, ionization, peculiar velocity, and spin temperature fields, which it then combines to compute the 21-cm brightness temperature. Although the physical processes are treated with approximate methods, we compare our results to a state-of-the-art large-scale hydrodynamic simulation, and find good agreement on scales pertinent to the upcoming observations (>~ 1 Mpc). The power spectra from 21cmFAST agree with those generated from the numerical simulation to within 10s of percent, down to the Nyquist frequency. We show results from a 1 Gpc simulation which tracks the cosmic 21-cm signal down from z=250, highlighting the various interesting epochs. Depending on the desired resolution, 21cmFAST can compute a redshift realization on a single processor in just a few minutes. Our code is fast, efficient, customizable and publicly available, making it a useful tool for 21-cm parameter studies.